Contemplating on installing a ESS 620 on my 2013 M3, since the 650 is not really that much more gains vs price. The question I have is how much more fuel consumption for a daily driver I should expect to see? As a law abide citizen of course

I think on my old stock 625 I got 19.6MPG on a 1000 mile drive, wrote it all down since changing the fuel injectors throws off the cars onboard MPG monitor and can't be used.
So steady at HWY speeds you might loose 2MPG or so vs stock

As a casual observer of the supercharger threads, this seems counter-intuitive. Sounds a lot like turbo lag to me...

Boost builds as the RPM's rise with a centrifugal supercharger...

A very simple division between the two is low-end power that drops off with a positive displacement superchargers vs. linear power with a centrifugal type supercharger that increases with engine rpm. The linear curve from a centrifugal supercharger compliments an engine’s existing power band, instead of working against it like a roots or twin-screw. Another significant benefit is that the efficiency of a centrifugal is much higher, meaning a smaller amount of the work that goes into turning the compressor gets converted to heat with a centrifugal vs. a positive displacement supercharger, and especially so vs. a roots type supercharger. So it takes less energy to make power with a centrifugal, and the power that is created is much more usable power.

A very simple division between the two is low-end power that drops off with a positive displacement superchargers vs. linear power with a centrifugal type supercharger that increases with engine rpm. The linear curve from a centrifugal supercharger compliments an engine’s existing power band, instead of working against it like a roots or twin-screw. Another significant benefit is that the efficiency of a centrifugal is much higher, meaning a smaller amount of the work that goes into turning the compressor gets converted to heat with a centrifugal vs. a positive displacement supercharger, and especially so vs. a roots type supercharger. So it takes less energy to make power with a centrifugal, and the power that is created is much more usable power.

I daily my 625 kitted car and get 13-14 avg mpg per the obd/stalk indicator. my commutes are in-town about 5-7 miles per day. if i go out on a drive with friends and play, it's in the 10-12 range.
I don't see the kits having much difference in mpg, when commuting my boost readings are less than 2 psi max boost(unless i have fun). Always go with the highest kit possible when purchasing the first time, it saves money in the long run and you will always want more power.

Contemplating on installing a ESS 620 on my 2013 M3, since the 650 is not really that much more gains vs price. The question I have is how much more fuel consumption for a daily driver I should expect to see? As a law abide citizen of course

This was one of the first things I noticed after having my kit installed. I went with AA, but I noticed a definite increase in fuel consumption.

So if the fuel consumption is not that much more I guess now is decision making ESS 625 or 650. Is the 650 really worth the money. I don't see too many of them in the forum 75% is ESS 625.

It's a tough call as you're paying $1,700 extra for +25HP and +10ft/lbs when looking at new. If you can find a used one that price split becomes even less so it would be worth it. You're also adding 1.5-2.0 PSI increase from 625 to the 650. I went with the 625/410 kit to get the best of both worlds: liquid intercooler and really solid numbers for $900 more than the 595/395 kit with slightly less boost.